Auxiliary Equations Approach for the Stochastic Unsteady Navier-Stokes Equations with Additive Random Noise

作     者：Wenju Zhao Max Gunzburger 

作者机构：Department of MathematicsSouthern University of Science and TechnologyShenzhenGuangdong 518055China Department of Scientific ComputingFlorida State UniversityTallahasseeFL 32304USA 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2020年第13卷第1期

页      面：1-26页

核心收录：

学科分类：0820[工学-石油与天然气工程] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This publication was supported in part by the US Air Force Office of Scientific Research grant FA9550-15-1-0001. 

主　　题：Stochastic Navier-Stokes equations Martingale regularization method Galerkin finite element method white noise 

摘      要：This paper presents a Martingale regularization method for the stochas-tic Navier–Stokes equations with additive noise.The original system is split into two equivalent parts,the linear stochastic Stokes equations with Martingale solution and the stochastic modified Navier–Stokes equations with relatively-higher regular-ities.Meanwhile,a fractional Laplace operator is introduced to regularize the noise term.The stability and convergence of numerical scheme for the pathwise modified Navier–Stokes equations are proved.The comparisons of non-regularized and reg-ularized noises for the Navier–Stokes system are numerically presented to further demonstrate the efficiency of our numerical scheme.